Introduction to Bayesian Statistics

Author: William M. Bolstad,James M. Curran

Publisher: John Wiley & Sons

ISBN: 1118593227

Category: Mathematics

Page: 624

View: 9817

"...this edition is useful and effective in teaching Bayesian inference at both elementary and intermediate levels. It is a well-written book on elementary Bayesian inference, and the material is easily accessible. It is both concise and timely, and provides a good collection of overviews and reviews of important tools used in Bayesian statistical methods." There is a strong upsurge in the use of Bayesian methods in applied statistical analysis, yet most introductory statistics texts only present frequentist methods. Bayesian statistics has many important advantages that students should learn about if they are going into fields where statistics will be used. In this third Edition, four newly-added chapters address topics that reflect the rapid advances in the field of Bayesian statistics. The authors continue to provide a Bayesian treatment of introductory statistical topics, such as scientific data gathering, discrete random variables, robust Bayesian methods, and Bayesian approaches to inference for discrete random variables, binomial proportions, Poisson, and normal means, and simple linear regression. In addition, more advanced topics in the field are presented in four new chapters: Bayesian inference for a normal with unknown mean and variance; Bayesian inference for a Multivariate Normal mean vector; Bayesian inference for the Multiple Linear Regression Model; and Computational Bayesian Statistics including Markov Chain Monte Carlo. The inclusion of these topics will facilitate readers' ability to advance from a minimal understanding of Statistics to the ability to tackle topics in more applied, advanced level books. Minitab macros and R functions are available on the book's related website to assist with chapter exercises. Introduction to Bayesian Statistics, Third Edition also features: Topics including the Joint Likelihood function and inference using independent Jeffreys priors and join conjugate prior The cutting-edge topic of computational Bayesian Statistics in a new chapter, with a unique focus on Markov Chain Monte Carlo methods Exercises throughout the book that have been updated to reflect new applications and the latest software applications Detailed appendices that guide readers through the use of R and Minitab software for Bayesian analysis and Monte Carlo simulations, with all related macros available on the book's website Introduction to Bayesian Statistics, Third Edition is a textbook for upper-undergraduate or first-year graduate level courses on introductory statistics course with a Bayesian emphasis. It can also be used as a reference work for statisticians who require a working knowledge of Bayesian statistics.
Posted in Mathematics

Introduction to Bayesian Statistics

Author: Karl-Rudolf Koch

Publisher: Springer Science & Business Media

ISBN: 3540727264

Category: Science

Page: 249

View: 6433

This book presents Bayes’ theorem, the estimation of unknown parameters, the determination of confidence regions and the derivation of tests of hypotheses for the unknown parameters. It does so in a simple manner that is easy to comprehend. The book compares traditional and Bayesian methods with the rules of probability presented in a logical way allowing an intuitive understanding of random variables and their probability distributions to be formed.
Posted in Science

Einführung in die Bayes-Statistik

Author: Karl-Rudolf Koch

Publisher: Springer-Verlag

ISBN: 3642569706

Category: Science

Page: 225

View: 8998

Das Buch führt auf einfache und verständliche Weise in die Bayes-Statistik ein. Ausgehend vom Bayes-Theorem werden die Schätzung unbekannter Parameter, die Festlegung von Konfidenzregionen für die unbekannten Parameter und die Prüfung von Hypothesen für die Parameter abgeleitet. Angewendet werden die Verfahren für die Parameterschätzung im linearen Modell, für die Parameterschätzung, die sich robust gegenüber Ausreißern in den Beobachtungen verhält, für die Prädiktion und Filterung, die Varianz- und Kovarianzkomponentenschätzung und die Mustererkennung. Für Entscheidungen in Systemen mit Unsicherheiten dienen Bayes-Netze. Lassen sich notwendige Integrale analytisch nicht lösen, werden numerische Verfahren mit Hilfe von Zufallswerten eingesetzt.
Posted in Science

Einführung in die Bayes-Statistik

Author: Karl-Rudolf Koch

Publisher: Springer

ISBN: 9783642630781

Category: Science

Page: 225

View: 5407

Das Buch führt auf einfache und verständliche Weise in die Bayes-Statistik ein. Ausgehend vom Bayes-Theorem werden die Schätzung unbekannter Parameter, die Festlegung von Konfidenzregionen für die unbekannten Parameter und die Prüfung von Hypothesen für die Parameter abgeleitet. Angewendet werden die Verfahren für die Parameterschätzung im linearen Modell, für die Parameterschätzung, die sich robust gegenüber Ausreißern in den Beobachtungen verhält, für die Prädiktion und Filterung, die Varianz- und Kovarianzkomponentenschätzung und die Mustererkennung. Für Entscheidungen in Systemen mit Unsicherheiten dienen Bayes-Netze. Lassen sich notwendige Integrale analytisch nicht lösen, werden numerische Verfahren mit Hilfe von Zufallswerten eingesetzt.
Posted in Science

Einführung in die Bayes-Statistik

Author: Karl-Rudolf Koch

Publisher: Springer

ISBN: 9783540666707

Category: Computers

Page: 225

View: 7457

Das Buch führt auf einfache und verständliche Weise in die Bayes-Statistik ein. Ausgehend vom Bayes-Theorem werden die Schätzung unbekannter Parameter, die Festlegung von Konfidenzregionen für die unbekannten Parameter und die Prüfung von Hypothesen für die Parameter abgeleitet. Angewendet werden die Verfahren für die Parameterschätzung im linearen Modell, für die Parameterschätzung, die sich robust gegenüber Ausreißern in den Beobachtungen verhält, für die Prädiktion und Filterung, die Varianz- und Kovarianzkomponentenschätzung und die Mustererkennung. Für Entscheidungen in Systemen mit Unsicherheiten dienen Bayes-Netze. Lassen sich notwendige Integrale analytisch nicht lösen, werden numerische Verfahren mit Hilfe von Zufallswerten eingesetzt.
Posted in Computers

An Introduction to Bayesian Analysis

Theory and Methods

Author: Jayanta K. Ghosh,Mohan Delampady,Tapas Samanta

Publisher: Springer Science & Business Media

ISBN: 0387354336

Category: Mathematics

Page: 354

View: 8385

This is a graduate-level textbook on Bayesian analysis blending modern Bayesian theory, methods, and applications. Starting from basic statistics, undergraduate calculus and linear algebra, ideas of both subjective and objective Bayesian analysis are developed to a level where real-life data can be analyzed using the current techniques of statistical computing. Advances in both low-dimensional and high-dimensional problems are covered, as well as important topics such as empirical Bayes and hierarchical Bayes methods and Markov chain Monte Carlo (MCMC) techniques. Many topics are at the cutting edge of statistical research. Solutions to common inference problems appear throughout the text along with discussion of what prior to choose. There is a discussion of elicitation of a subjective prior as well as the motivation, applicability, and limitations of objective priors. By way of important applications the book presents microarrays, nonparametric regression via wavelets as well as DMA mixtures of normals, and spatial analysis with illustrations using simulated and real data. Theoretical topics at the cutting edge include high-dimensional model selection and Intrinsic Bayes Factors, which the authors have successfully applied to geological mapping. The style is informal but clear. Asymptotics is used to supplement simulation or understand some aspects of the posterior.
Posted in Mathematics

A Student’s Guide to Bayesian Statistics

Author: Ben Lambert

Publisher: SAGE

ISBN: 1526418266

Category: Social Science

Page: 520

View: 8547

Supported by a wealth of learning features, exercises, and visual elements as well as online video tutorials and interactive simulations, this book is the first student-focused introduction to Bayesian statistics. Without sacrificing technical integrity for the sake of simplicity, the author draws upon accessible, student-friendly language to provide approachable instruction perfectly aimed at statistics and Bayesian newcomers. Through a logical structure that introduces and builds upon key concepts in a gradual way and slowly acclimatizes students to using R and Stan software, the book covers: An introduction to probability and Bayesian inference Understanding Bayes' rule Nuts and bolts of Bayesian analytic methods Computational Bayes and real-world Bayesian analysis Regression analysis and hierarchical methods This unique guide will help students develop the statistical confidence and skills to put the Bayesian formula into practice, from the basic concepts of statistical inference to complex applications of analyses.
Posted in Social Science

An Introduction to Bayesian Inference in Econometrics

Author: Arnold Zellner

Publisher: Wiley-Interscience

ISBN: 9780471169376

Category: Mathematics

Page: 448

View: 6903

This is a classical reprint edition of the original 1971 edition of An Introduction to Bayesian Inference in Economics. This historical volume is an early introduction to Bayesian inference and methodology which still has lasting value for today's statistician and student. The coverage ranges from the fundamental concepts and operations of Bayesian inference to analysis of applications in specific econometric problems and the testing of hypotheses and models.
Posted in Mathematics

Bayes' Rule

A Tutorial Introduction to Bayesian Analysis

Author: James V. Stone

Publisher: Sebtel Press

ISBN: 0956372848

Category: Bayesian statistical decision theory

Page: 170

View: 733

In this richly illustrated book, a range of accessible examples are used to show how Bayes' rule is actually a natural consequence of commonsense reasoning. The tutorial style of writing, combined with a comprehensive glossary, makes this an ideal primer for the novice who wishes to become familiar with the basic principles of Bayesian analysis.
Posted in Bayesian statistical decision theory

The BUGS Book

A Practical Introduction to Bayesian Analysis

Author: David Lunn,Chris Jackson,Nicky Best,Andrew Thomas,David Spiegelhalter

Publisher: CRC Press

ISBN: 1466586664

Category: Mathematics

Page: 399

View: 5946

Bayesian statistical methods have become widely used for data analysis and modelling in recent years, and the BUGS software has become the most popular software for Bayesian analysis worldwide. Authored by the team that originally developed this software, The BUGS Book provides a practical introduction to this program and its use. The text presents complete coverage of all the functionalities of BUGS, including prediction, missing data, model criticism, and prior sensitivity. It also features a large number of worked examples and a wide range of applications from various disciplines. The book introduces regression models, techniques for criticism and comparison, and a wide range of modelling issues before going into the vital area of hierarchical models, one of the most common applications of Bayesian methods. It deals with essentials of modelling without getting bogged down in complexity. The book emphasises model criticism, model comparison, sensitivity analysis to alternative priors, and thoughtful choice of prior distributions—all those aspects of the "art" of modelling that are easily overlooked in more theoretical expositions. More pragmatic than ideological, the authors systematically work through the large range of "tricks" that reveal the real power of the BUGS software, for example, dealing with missing data, censoring, grouped data, prediction, ranking, parameter constraints, and so on. Many of the examples are biostatistical, but they do not require domain knowledge and are generalisable to a wide range of other application areas. Full code and data for examples, exercises, and some solutions can be found on the book’s website.
Posted in Mathematics

Introduction to Bayesian Estimation and Copula Models of Dependence

Author: Arkady Shemyakin,Alexander Kniazev

Publisher: John Wiley & Sons

ISBN: 1118959019

Category: Mathematics

Page: 352

View: 9236

Presents an introduction to Bayesian statistics, presents an emphasis on Bayesian methods (prior and posterior), Bayes estimation, prediction, MCMC,Bayesian regression, and Bayesian analysis of statistical modelsof dependence, and features a focus on copulas for risk management Introduction to Bayesian Estimation and Copula Models of Dependence emphasizes the applications of Bayesian analysis to copula modeling and equips readers with the tools needed to implement the procedures of Bayesian estimation in copula models of dependence. This book is structured in two parts: the first four chapters serve as a general introduction to Bayesian statistics with a clear emphasis on parametric estimation and the following four chapters stress statistical models of dependence with a focus of copulas. A review of the main concepts is discussed along with the basics of Bayesian statistics including prior information and experimental data, prior and posterior distributions, with an emphasis on Bayesian parametric estimation. The basic mathematical background of both Markov chains and Monte Carlo integration and simulation is also provided. The authors discuss statistical models of dependence with a focus on copulas and present a brief survey of pre-copula dependence models. The main definitions and notations of copula models are summarized followed by discussions of real-world cases that address particular risk management problems. In addition, this book includes: • Practical examples of copulas in use including within the Basel Accord II documents that regulate the world banking system as well as examples of Bayesian methods within current FDA recommendations • Step-by-step procedures of multivariate data analysis and copula modeling, allowing readers to gain insight for their own applied research and studies • Separate reference lists within each chapter and end-of-the-chapter exercises within Chapters 2 through 8 • A companion website containing appendices: data files and demo files in Microsoft® Office Excel®, basic code in R, and selected exercise solutions Introduction to Bayesian Estimation and Copula Models of Dependence is a reference and resource for statisticians who need to learn formal Bayesian analysis as well as professionals within analytical and risk management departments of banks and insurance companies who are involved in quantitative analysis and forecasting. This book can also be used as a textbook for upper-undergraduate and graduate-level courses in Bayesian statistics and analysis. ARKADY SHEMYAKIN, PhD, is Professor in the Department of Mathematics and Director of the Statistics Program at the University of St. Thomas. A member of the American Statistical Association and the International Society for Bayesian Analysis, Dr. Shemyakin's research interests include informationtheory, Bayesian methods of parametric estimation, and copula models in actuarial mathematics, finance, and engineering. ALEXANDER KNIAZEV, PhD, is Associate Professor and Head of the Department of Mathematics at Astrakhan State University in Russia. Dr. Kniazev's research interests include representation theory of Lie algebras and finite groups, mathematical statistics, econometrics, and financial mathematics.
Posted in Mathematics

Introduction to Applied Bayesian Statistics and Estimation for Social Scientists

Author: Scott M. Lynch

Publisher: Springer Science & Business Media

ISBN: 0387712658

Category: Social Science

Page: 359

View: 7779

This book outlines Bayesian statistical analysis in great detail, from the development of a model through the process of making statistical inference. The key feature of this book is that it covers models that are most commonly used in social science research - including the linear regression model, generalized linear models, hierarchical models, and multivariate regression models - and it thoroughly develops each real-data example in painstaking detail.
Posted in Social Science

Bayesian statistics

principles, models, and applications

Author: S. James Press

Publisher: John Wiley & Sons Inc

ISBN: N.A

Category: Mathematics

Page: 237

View: 8956

An introduction to Bayesian statistics, with emphasis on interpretation of theory, and application of Bayesian ideas to practical problems. First part covers basic issues and principles, such as subjective probability, Bayesian inference and decision making, the likelihood principle, predictivism, and numerical methods of approximating posterior distributions, and includes a listing of Bayesian computer programs. Second part is devoted to models and applications, including univariate and multivariate regression models, the general linear model, Bayesian classification and discrimination, and a case study of how disputed authorship of some of the Federalist Papers was resolved via Bayesian analysis. Includes biographical material on Thomas Bayes, and a reproduction of Bayes's original essay. Contains exercises.
Posted in Mathematics

Introduction to Bayesian Econometrics

Author: Edward Greenberg

Publisher: Cambridge University Press

ISBN: 1107015316

Category: Business & Economics

Page: 249

View: 2039

This textbook explains the basic ideas of subjective probability and shows how subjective probabilities must obey the usual rules of probability to ensure coherency. It defines the likelihood function, prior distributions and posterior distributions. It explains how posterior distributions are the basis for inference and explores their basic properties. Various methods of specifying prior distributions are considered, with special emphasis on subject-matter considerations and exchange ability. The regression model is examined to show how analytical methods may fail in the derivation of marginal posterior distributions. The remainder of the book is concerned with applications of the theory to important models that are used in economics, political science, biostatistics and other applied fields. New to the second edition is a chapter on semiparametric regression and new sections on the ordinal probit, item response, factor analysis, ARCH-GARCH and stochastic volatility models. The new edition also emphasizes the R programming language.
Posted in Business & Economics

Reasoning with Data

An Introduction to Traditional and Bayesian Statistics Using R

Author: Jeffrey M. Stanton

Publisher: Guilford Publications

ISBN: 1462530265

Category: Computers

Page: 325

View: 512

Engaging and accessible, this book teaches readers how to use inferential statistical thinking to check their assumptions, assess evidence about their beliefs, and avoid overinterpreting results that may look more promising than they really are. It provides step-by-step guidance for using both classical (frequentist) and Bayesian approaches to inference. Statistical techniques covered side by side from both frequentist and Bayesian approaches include hypothesis testing, replication, analysis of variance, calculation of effect sizes, regression, time series analysis, and more. Students also get a complete introduction to the open-source R programming language and its key packages. Throughout the text, simple commands in R demonstrate essential data analysis skills using real-data examples. The companion website (www.guilford.com/stanton2-materials) provides annotated R code for the book's examples, in-class exercises, supplemental reading lists, and links to online videos, interactive materials, and other resources. Pedagogical Features: *Playful, conversational style and gradual approach; suitable for students without strong math backgrounds. *End-of-chapter exercises based on real data supplied in the free R package. *Technical explanation and equation/output boxes. *Appendices on how to install R and work with the sample datasets.
Posted in Computers

Statistik-Workshop für Programmierer

Author: Allen B. Downey

Publisher: O'Reilly Germany

ISBN: 3868993436

Category: Computers

Page: 160

View: 4916

Wenn Sie programmieren können, beherrschen Sie bereits Techniken, um aus Daten Wissen zu extrahieren. Diese kompakte Einführung in die Statistik zeigt Ihnen, wie Sie rechnergestützt, anstatt auf mathematischem Weg Datenanalysen mit Python durchführen können. Praktischer Programmier-Workshop statt grauer Theorie: Das Buch führt Sie anhand eines durchgängigen Fallbeispiels durch eine vollständige Datenanalyse -- von der Datensammlung über die Berechnung statistischer Kennwerte und Identifikation von Mustern bis hin zum Testen statistischer Hypothesen. Gleichzeitig werden Sie mit statistischen Verteilungen, den Regeln der Wahrscheinlichkeitsrechnung, Visualisierungsmöglichkeiten und vielen anderen Arbeitstechniken und Konzepten vertraut gemacht. Statistik-Konzepte zum Ausprobieren: Entwickeln Sie über das Schreiben und Testen von Code ein Verständnis für die Grundlagen von Wahrscheinlichkeitsrechnung und Statistik: Überprüfen Sie das Verhalten statistischer Merkmale durch Zufallsexperimente, zum Beispiel indem Sie Stichproben aus unterschiedlichen Verteilungen ziehen. Nutzen Sie Simulationen, um Konzepte zu verstehen, die auf mathematischem Weg nur schwer zugänglich sind. Lernen Sie etwas über Themen, die in Einführungen üblicherweise nicht vermittelt werden, beispielsweise über die Bayessche Schätzung. Nutzen Sie Python zur Bereinigung und Aufbereitung von Rohdaten aus nahezu beliebigen Quellen. Beantworten Sie mit den Mitteln der Inferenzstatistik Fragestellungen zu realen Daten.
Posted in Computers

An Introduction to Bayesian Inference and Decision

Author: Robert L. Winkler

Publisher: Probabilistic Pub

ISBN: 9780964793842

Category: Mathematics

Page: 452

View: 9553

CD-ROM contains: Beta Distribution Generator (Excel file) ; Binomial Distribution Generator (Excel file) ; book exercises (MS Word files) ; book figures (Powerpoint files) ; TreeAge Data decision trees for some of the examples in the book ; Demonstration versions of TreeAge Data and Lumina Analytica.
Posted in Mathematics

Die Berechnung der Zukunft

Warum die meisten Prognosen falsch sind und manche trotzdem zutreffen - Der New York Times Bestseller

Author: Nate Silver

Publisher: Heyne Verlag

ISBN: 3641112702

Category: Business & Economics

Page: 656

View: 9453

Zuverlässige Vorhersagen sind doch möglich! Nate Silver ist der heimliche Gewinner der amerikanischen Präsidentschaftswahlen 2012: ein begnadeter Statistiker, als »Prognose-Popstar« und »Wundernerd« weltberühmt geworden. Er hat die Wahlergebnisse aller 50 amerikanischen Bundesstaaten absolut exakt vorausgesagt – doch damit nicht genug: Jetzt zeigt Nate Silver, wie seine Prognosen in Zukunft Terroranschläge, Umweltkatastrophen und Finanzkrisen verhindern sollen. Gelingt ihm die Abschaffung des Zufalls? Warum werden Wettervorhersagen immer besser, während die Terrorattacken vom 11.09.2001 niemand kommen sah? Warum erkennen Ökonomen eine globale Finanzkrise nicht einmal dann, wenn diese bereits begonnen hat? Das Problem ist nicht der Mangel an Informationen, sondern dass wir die verfügbaren Daten nicht richtig deuten. Zuverlässige Prognosen aber würden uns helfen, Zufälle und Ungewissheiten abzuwehren und unser Schicksal selbst zu bestimmen. Nate Silver zeigt, dass und wie das geht. Erstmals wendet er seine Wahrscheinlichkeitsrechnung nicht nur auf Wahlprognosen an, sondern auf die großen Probleme unserer Zeit: die Finanzmärkte, Ratingagenturen, Epidemien, Erdbeben, den Klimawandel, den Terrorismus. In all diesen Fällen gibt es zahlreiche Prognosen von Experten, die er überprüft – und erklärt, warum sie meist falsch sind. Gleichzeitig schildert er, wie es gelingen kann, im Rauschen der Daten die wesentlichen Informationen herauszufiltern. Ein unterhaltsamer und spannender Augenöffner!
Posted in Business & Economics

Introduction to WinBUGS for Ecologists

Bayesian Approach to Regression, ANOVA, Mixed Models and Related Analyses

Author: Marc Kery

Publisher: Academic Press

ISBN: 9780123786067

Category: Science

Page: 320

View: 6484

Introduction to WinBUGS for Ecologists introduces applied Bayesian modeling to ecologists using the highly acclaimed, free WinBUGS software. It offers an understanding of statistical models as abstract representations of the various processes that give rise to a data set. Such an understanding is basic to the development of inference models tailored to specific sampling and ecological scenarios. The book begins by presenting the advantages of a Bayesian approach to statistics and introducing the WinBUGS software. It reviews the four most common statistical distributions: the normal, the uniform, the binomial, and the Poisson. It describes the two different kinds of analysis of variance (ANOVA): one-way and two- or multiway. It looks at the general linear model, or ANCOVA, in R and WinBUGS. It introduces generalized linear model (GLM), i.e., the extension of the normal linear model to allow error distributions other than the normal. The GLM is then extended contain additional sources of random variation to become a generalized linear mixed model (GLMM) for a Poisson example and for a binomial example. The final two chapters showcase two fairly novel and nonstandard versions of a GLMM. The first is the site-occupancy model for species distributions; the second is the binomial (or N-) mixture model for estimation and modeling of abundance. Introduction to the essential theories of key models used by ecologists Complete juxtaposition of classical analyses in R and Bayesian analysis of the same models in WinBUGS Provides every detail of R and WinBUGS code required to conduct all analyses Companion Web Appendix that contains all code contained in the book and additional material (including more code and solutions to exercises)
Posted in Science

Bayes' Rule with MatLab

A Tutorial Introduction to Bayesian Analysis

Author: James V Stone

Publisher: N.A

ISBN: 9780993367908

Category: Mathematics

Page: 192

View: 5233

Discovered by an 18th century mathematician and preacher, Bayes' rule is a cornerstone of modern probability theory. In this richly illustrated book, a range of accessible examples is used to show how Bayes' rule is actually a natural consequence of common sense reasoning. Bayes' rule is then derived using intuitive graphical representations of probability, and Bayesian analysis is applied to parameter estimation using the MatLab and Python programs provided online. The tutorial style of writing, combined with a comprehensive glossary, makes this an ideal primer for novices who wish to become familiar with the basic principles of Bayesian analysis. Note that this MatLab version of Bayes' Rule includes working MatLab code snippets alongside the relevant equations.
Posted in Mathematics